How can I rewrite the inequality 12x + 2y < 42 in slope-intercept form?

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To rewrite the inequality 12x + 2y < 42 in slope-intercept form (which is generally written as y < mx + b, where m is the slope and b is the y-intercept), we need to isolate y on one side of the inequality.

Here are the steps:

  1. Start with the original inequality:

    12x + 2y < 42

  2. First, subtract 12x from both sides to help isolate y:

    2y < -12x + 42

  3. Next, divide every term in the inequality by 2 to solve for y:

    4. y < -6x + 21

  4. Now the inequality is in slope-intercept form, where:
    • m = -6 (the slope)
    • b = 21 (the y-intercept)

In summary, the inequality 12x + 2y < 42 rewritten in slope-intercept form is:

y < -6x + 21

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